CALIBRATION OF A NOVEL SIX-DEGREE-OF-FREEDOM FORCE / TORQUE MEASUREMENT SYSTEM

Transcription

1 Measurement of Mass, Force and Torque (APMF 23) International Journal of Modern Physics: Conference Series Vol. 24 (23) 367 (9 pages) The Authors DOI:.42/S CALIBRATION OF A NOVEL SIX-DEGREE-OF-FREEDOM FORCE / TORQUE MEASUREMENT SYSTEM JAN SCHLEICHERT Institute of Process Measurement and Sensor Technology, Department of Mechanical Engineering, Ilmenau, University of Technology, P.O. Box Ilmenau, Germany jan.schleichert@tu-ilmenau.de ILKO RAHNEBERG Institute of Process Measurement and Sensor Technology, Department of Mechanical Engineering, Ilmenau, University of Technology, P.O. Box Ilmenau, Germany ilko.rahneberg@tu-ilmenau.de THOMAS FRÖHLICH Institute of Process Measurement and Sensor Technology, Department of Mechanical Engineering, Ilmenau, University of Technology, P.O. Box Ilmenau, Germany thomas.froehlich@tu-ilmenau.de Multi-component force/torque transducers are used in a large field of scientific and industrial applications like robotics, biomechanics and even fluid mechanics. These sensors need to be calibrated for traceable measurements. As the calibration procedure determines the measurement uncertainty, it plays an important role in sensor development for reaching the required measurement specifications. For the application in local Lorentz Force Velocimetry (Ref. ) a six degree of freedom force/torque sensor for measurement ranges of ±.2 N and ± 5 mnm was developed. This sensor can also be adapted to other applications that require multi-dimensional force/torque feedback in the µn- and µnm-range such as tactile dimensional measurements and micro-manipulation. This paper discusses the calibration and the evaluation of the properties of the calibration device and the calibration procedure of the sensor system. After a brief introduction of the sensor design and its working principle the calibration setup is described and the uncertainty contributions to the forces and torques are calculated. Then the calibration procedure is presented and the resulting output signals of the sensor are depicted. As a result of the calibration, the calibration matrix is given with a discussion of its major components. Keywords: Multi-component force/torque measurement; 6-DoF calibration procedures; sensor development. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 3. (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. 367-

2 J. Schleichert, I. Rahneberg & T. Fröhlich. Introduction For the measurement of force and torque in all spatial directions, a novel design for a sixdegree-of-freedom force/torque sensor was developed and patented in Ref. 2. The sensor was designed to measure force in the range of ±.2 N and torque in the range of ± 5 mnm with a theoretical resolution of 2 µn and.5 µnm respectively. With these specifications it covers the field between commercially available (Ref. 3) and micro fabricated Six-DoF-force/torque sensors (Ref. 4). The calibration of multi-component sensors in this range cannot be done easily with available sensors as reference. Thus, a specific calibration system had to be developed that allows a full calibration of the sensor with a relative uncertainty of Measurement System The basic principle of the measurement system is a parallel-spring mechanism as shown in Fig. left. It allows the measurement of one force component by transforming the applied force into strains (, ) at the four flexure hinges. These strains can be measured using strain gauges in a full bridge arrangement shown in Fig. (left). The measurement principle for the torque can be understood by the definition of torque as a couple of forces. Consequently, two parallel springs can be used to measure a torque as shown in Fig. (right). Fig.. Basic structure of the measurement principle for measurement of force (left) and torque (right). The measurement of three force components can be performed by connecting three parallel springs in orthogonal directions. The torques can be measured by adding another three parallel springs. The resulting setup is illustrated in Fig. 2. Fig. 2. Left: Measurement principle of 6-DoF force/torque sensor, right: basic sensor design

3 Calibration of a Novel 6-DoF Force / Torque Measurement System This design has isotropic properties and has the advantage that the measurement range of force and torque can be defined independently by adapting the design parameters which are the distance of the parallel springs and the thickness of the flexure hinges. 3. Design of Calibration System During the calibration forces in all three directions of the axes of a Cartesian coordinate system and according torques around these axes have to be applied with a relative uncertainty of -3. When taking into account the nominal forces and torques this leads to forces of ± 2-4 N and torques of ± 5-6 Nm. The calibration of the forces can be done in the earth s gravity field by placing weights onto the sensor. The sensor is mounted in a calibration platform, so that the measurements can be done with different orientations of the sensor to calibrate all force components. The resulting force applied to the sensor is given by Fm g cos m g cos, () where m is a calibrated mass, g is the local gravitational constant and the angles and are deviations of the sensor alignment to the horizontal plane. In order to reduce the cross-coupling between the forces, these angles have to be adjusted to zero. The torque can be calibrated similarly by adding a lever of the length l between the feed-in and the force according to Eq. (2): MFlm g l cosγ. (2) Additional to the requirements of the force calibration, the length of the lever l is required for calculating the torque. Since the results of the calibration are sensitivities, only changes of torque have to be applied with the required uncertainty. Therefore, an exact placing of the weights on the lever is crucial. Here, spheres with a calibrated mass are used as weights. Spheres can be produced with a high accuracy and they can be placed into holes with high repeatability. The calibration lever contains holes for generating ten different torque steps using one sphere. The lever has to be designed for low deformations, but needs to be light enough not to exceed the nominal load of the sensor with the sphere placed. To reduce manufacturing-tolerances, the calibration system was fabricated by wire-erosion. The Alignment of the sensor s measurement axes and the direction of gravitational acceleration was done with a calibration platform that was designed to allow turning and tilting of the sensor. Fig. 3. Torque calibration principle and angular deviations from horizontal plane

4 J. Schleichert, I. Rahneberg & T. Fröhlich Fig. 4. Six-DoF force/torque sensor () mounted in calibration platform (2) with the calibration lever (3) assembled to the force feed-in. A sphere (4) is placed, to create a torque around the z-axis of the sensor. The letters A, B and C describe the different sides of the lever. The deviations of the positioning of the spheres in the lever were measured on the coordinate measuring machine Zeiss UMM55 with a position resolution of. µm. By replacing the spheres several times and measuring their position, the mean value of the positioning as well as the repeatability of placing the spheres could be determined. For every side of the lever, the deviations from the effective length and the deviations from the distance to the mounting point are shown in Fig. 5. Standard deviation of the positioning in mm x x -3 Az Ax x x -3 By Bx x Cz -2 - x Cx Nominal Positions Fig. 5. Standard deviation of placing spheres into the holes against the nominal position

5 Calibration of a Novel 6-DoF Force / Torque Measurement System From the manufacturing of the lever, the maximum relative error of the position of the holes in the lever is.3-3. For the repeated positioning of the spheres, the maximum relative uncertainty is The sphere was weighted ten times using a Sartorius MC 2 S with a resulting uncertainty of 2-8 kg. The calibration of force and torque was carried out in a climate control chamber which ensures temperature stability of. K. With the thermal expansion coefficient of aluminum, this leads to a relative uncertainty of the length of the lever of The maximum change in the position of the sphere caused by deformations of the calibration lever was calculated using FEM. With a value of 5-8 m, this effect is negligible for the following considerations. The angular deviations caused by the deformation of the sensor at the maximum torque were also calculated in FEM. With values of rad, they were neglected as well. The angular adjustment of the sensor axes into the direction of gravitational acceleration was done with the calibration platform shown in Fig. 4 using a spirit level. The angles and describe the deviations from the adjustment of the sensor in the horizontal plane. By using a spirit level, the alignment can be done with uncertainties in the range of.5-3 rad. This was verified with a coincidence level, having a resolution of -5 rad. With the calculation according to Ref. 8, a relative uncertainty for the angular adjustment of is obtained. The uncertainty contributions and resulting uncertainty for the force and torque are given in Table. The uncertainty of the torque is much higher than that of the force, caused by the uncertainty contribution of the effective length of the lever. These uncertainties lie below the design limits for the calibration device. Table. Contributions and resulting uncertainty for force and torque created with the calibration system. Quantity Reference value Standard uncertainty Relative uncertainty m kg 2-8 kg g 9.8 m/ * 2-6 m/ 2-6 l -3 m m γ x rad.5-3 rad γ z rad.5-3 rad Relative uncertainty of force (k = 2) Relative uncertainty of torque (k = 2) Calibration Procedure As the strain gauge sensor transfers forces and torques into voltage signals, calibration factors are required to calculate the acting forces and torques. Because the sensor used is a monolithic structure, forces and torques cause mutual interferences. When assuming a linear behavior, a multi-component sensor can be described with Eq. (3) (Ref. 5). UC F C F, (3) * Local Gravity for Ilmenau, Germany taken from Gravity Information System, Physikalisch-Technische Bundesanstalt, Germany (

6 J. Schleichert, I. Rahneberg & T. Fröhlich where is a vector of acting force and torque components, U the measured output signal vector and C the compliance matrix. This matrix needs to be determined by calibration. Therefore, the output signals U c of the sensor resulting from a known loading are measured and used for the calculation according to Eq. (4): CU c F c -. (4) With the calibration matrix given, the force and torque vectors can be calculated in case of a minimal sensor that has an equal number of output and input signals by multiplication of the inverse compliance matrix C - with the measured output signals: FC - U. (5) For redundant sensors, the number of strain gauge bridges is higher than the number of degrees-of-freedom, so that C is a non-square matrix that can be inverted only approximately, for example by taking the Moore-Penrose Inverse CMC T C- CT. For the calibration and additional investigation of the linearity of the sensor, a multipoint loading method with five different loads distributed over the measurement range of the sensor was used. The Calibration Procedure follows the proposals of Ref. 6 and allows the calculation of the calibration coefficients contained in the compliance matrix, as well as the uncertainty contributions of reproducibility, repeatability, creeping behavior, hysteresis error, zero-point drift and interpolation. The loading procedure shown in Fig. 6 begins with a preloading () that is needed to have a defined starting point for the calibration. After three minutes relaxation time in which the creeping of the sensor can be determined, two series of upward loadings (2) are applied in the same mounting position to identify the repeatability of the measurements. Then the sensor is remounted, preloaded and calibrated with an upward and downward loading twice (3) to calculate the reproducibility and the hysteresis error of the measurements with the sensor. The zeropoint deviation is the difference between the zero point before and after a loading set. For the interpolation error, the estimate for a single load step is compared with the linear interpolation between different load steps Applied load / nominal load Time in s Fig. 6. Applied load during calibration procedure for force components

7 Calibration of a Novel 6-DoF Force / Torque Measurement System The signals of the strain gauge bridges during the loading are depicted in Fig. 7. As can be seen here, besides the main output for the applied load component, there are also changes in the other components due to cross-coupling. Fig. 7. Calibration procedure for force components, exemplarily shown for force Fz. To reduce the uncertainty contribution of the measurement electronics, the electrical signals were filtered. The Allan Standard deviation was calculated to find the optimal filtering time-constant τ, showing a minimum of -8 V/V. This is resulting in a relative standard deviation of 2-4. Longer filtering time leads to an increase of the standard deviation due to drift of the signal. Fig. 8. Allan Standard deviation for the output signal of a measurement bridge

8 J. Schleichert, I. Rahneberg & T. Fröhlich 5. Results of Calibration As a result of the calibration, the calibration matrix was determined from Eq. (4), inverted, and shown in a dimensionless form by dividing all force components by the maximum force sensitivity according to Eq. (6) and all torque components by the maximum torque sensitivity after Eq. (7):,,, - i 3, j 6 (6),,, - r4 6, s 6 (7) Here, the main sensitivities for force and torque can be seen on the main diagonal. The deviation in sensitivity between the main force components is less than 6% and between the main torque components less than 2%. The cross-coupling between the components is less than.2% for the forces and less than 3% for the torques. The calibration loads for the x and y components of force cannot be introduced into the force feed-in without having a spatial distance which causes a parasitic torque. This effect can be seen in the calibration matrix at the coefficients and. Both force components have an almost equal cross-coupling to a torque component. Only the forces in the z-axis can be calibrated without cross-coupling onto a torque component. 6. Conclusion In this paper, a design of a calibration device for a 6-DoF force/torque measurement system for forces in the range of ±.2 N and torques of ± 5 mnm is described. The repeatability of the positioning of spheres on the calibration lever and the resulting uncertainty contribution for force and torque application are investigated. The results are used to calculate the uncertainty of the calibration force and torque applied with the calibration device. After that, the calibration procedure for the 6-DoF force/torque sensor is described and the resulting output signals of the sensor are shown for an exemplary case. The Allan standard deviation is used as a method to find an appropriate filtering time-constant to improve the resolution of measurement. As a result of the calibration process, the calibration matrix is given and the matrix elements are discussed

9 Calibration of a Novel 6-DoF Force / Torque Measurement System Acknowledgments The authors gratefully acknowledge the contributions of Falko Hilbrunner to the sensor design and of Roland Füssl to the position measurements. This work was financially supported from the Deutsche Forschungsgemeinschaft in the framework of the Research Training Group Lorentz Force Velocimetry and Lorentz Force Eddy Current Testing (grant GRK 567/). References. C. Heinicke, S. Tympel, G. Pulugundla, I. Rahneberg, T. Boeck, A. Thess, Interaction of a small permanent magnet with a liquid metal duct flow, J. Appl. Phys. 2, 2494 (22). 2. I. Rahneberg, F. Hilbrunner,T. Fröhlich, Patent: Vorrichtung zur simultanen Erfassung von Kraft- und Momentenkomponenten, DE N.N. Datasheet: Nano 7, ATI Industrial Automation, Apex, NC USA, 2 4. F. Beyeler, S. Muntwyler, B. J. Nelson, Design and Calibration of a Microfabricated 6-Axis Force-Torque Sensor for Microrobotic Applications (Best Automation Paper and Best Student Paper Award), Proc. IEEE International Conference on Robotics and Automation (ICRA), Kobe, Japan, May A. Bicci: A Criterion for the Optimal Design of. Multi-Axis Force Sensors, A.I. Memo No. 263, Massachusetts Institute of Technology, Deutscher Kalibrierdienst DKD: Richtlinie DKD-R 3.3 Kalibrierung von Kraftmessgeräten, Ausgabe 3/27, Braunschweig 7. DIN EN ISO 376: Metallische Werkstoffe - Kalibrierung der Kraftmessgeräte für die Prüfung von Prüfmaschinen mit einachsiger Beanspruchung, Beuth Verlag Berlin, Ausgabe D. Röske: Uncertainty contribution in the case of cosine function with zero estimate a proposal, IMEKO 2 TC3, TC5 and TC22 Conferences Metrology in Modern Context, 2, Pattaya, Chonburi, Thailand 367-9